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“On the advice of his doctor, the prime minister has tonight been admitted to hospital for tests,” a spokesman said Sunday. “This is a precautionary step, as the prime minister continues to have persistent symptoms of coronavirus 10 days after testing positive for the virus.”

The queen called it “a time of disruption in the life of our country: a disruption that has brought grief to some, financial difficulties to many, and enormous changes to the daily lives of us all.”

It is only the fourth time in her 66-year reign that the queen has addressed the British people, apart from her annual Christmas greeting — and it carries a distinct echo of the celebrated radio address her father, George VI, delivered in September 1939, as Britain stood on the brink of war with Germany.

“I hope in the years to come, everyone will be able to take pride in how they responded to this challenge,” the queen said, “and those who come after us will say that the Britons of this generation were as strong as any. That the attributes of self-discipline, of quiet good-humored resolve and of fellow-feeling still characterize this country.”

Mr. Johnson had been in isolation in his residence next door to 10 Downing Street.

On Saturday, his 32-year-old girlfriend, Carrie Symonds, disclosed that she, too, is suffering symptoms. Ms. Symonds is pregnant.

The British foreign secretary, Dominic Raab, is expected to lead the daily cabinet meeting on the pandemic on Monday. Under the government’s succession plan, Mr. Raab would take up Mr. Johnson’s duties if he is incapacitated.

President Trump expressed his well wishes to Mr. Johnson during a White Houses briefing on Sunday.

“All Americans are praying for him,” Mr. Trump said. “He’s a strong man, strong person.”